Numerical analysis of the Landau-Lifshitz-Gilbert equation with inertial effects

Ruggeri, Michele (2022) Numerical analysis of the Landau-Lifshitz-Gilbert equation with inertial effects. ESAIM: Mathematical Modelling and Numerical Analysis, 56 (4). pp. 1199-1222. ISSN 0764-583X (https://doi.org/10.1051/m2an/2022043)

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Abstract

We consider the numerical approximation of the inertial Landau-Lifshitz-Gilbert equation (iLLG), which describes the dynamics of the magnetisation in ferromagnetic materials at subpicosecond time scales. We propose and analyse two fully discrete numerical schemes: The first method is based on a reformulation of the problem as a linear constrained variational formulation for the linear velocity. The second method exploits a reformulation of the problem as a first order system in time for the magnetisation and the angular momentum. Both schemes are implicit, based on first-order finite elements, and generate approximations satisfying the unit-length constraint of iLLG at the vertices of the underlying mesh. For both methods, we prove convergence of the approximations towards a weak solution of the problem. Numerical experiments validate the theoretical results and show the applicability of the methods for the simulation of ultrafast magnetic processes.

  • Item type:Article
    ID code:80625
    Dates:
    Date
    Event
    27 June 2022
    Published
    27 April 2022
    Published Online
    26 April 2022
    Accepted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:10 May 2022 10:25
    Last modified:09 Apr 2024 03:12
    URI:https://strathprints.strath.ac.uk/id/eprint/80625
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